78.11.15 problem 10 (c, n=3)

Internal problem ID [18286]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 10 (c, n=3)
Date solved : Tuesday, January 28, 2025 at 11:45:11 AM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(x*diff(y(x),x$2)-(x+3)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{1} +c_{2} \left (x^{3}+3 x^{2}+6 x +6\right ) \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 29

DSolve[x*D[y[x],{x,2}] -(x+3)*D[y[x],x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x-c_2 \left (x^3+3 x^2+6 x+6\right ) \]